Prepare the cabbages leaves. Some cooks find that putting the whole cabbage into the freezer makes the leaves pliable when it is removed and thawed. Others boil the whole cabbage in salted boiling water for 1 minute, then remove leaves and press them to remove as much water as possible, then freeze and thaw. Either way, separate the softened leaves, keeping them as whole as possible. Smaller or torn leaves can be used to line the baking pan.
Cook the rice in salted water with the vegetable oil until it is just done; do not overcook. Drain completely if all the water is not absorbed.
Preheat oven to 350 F. Grease a 9” x 13” baking pan with margarine or oil.
Heat the remaining oil in a large skillet. Add the garlic and onion, and sauté over medium heat until soft and fragrant, about 2 minutes. Add the ground meat; stir and toss until it is thoroughly cooked, about 5 minutes. Add the rice and stir to combine. Reserve about ¾ cup of tomato sauce. Add the rest of the tomato sauce, parsley, salt, pepper, herbs and spices, and stir to combine. Reduce heat to low; simmer for about 20 minutes until all the sauce is absorbed and the mixture is fairly cohesive. Taste and adjust seasonings.
Spread your prepared cabbage leaves on a table; you should have about two dozen leaves. Use any extra leaves to line the casserole; pour a quarter cup of the reserved tomato sauce over the bottom.
Place about a tablespoon of filling on the center of each leaf; roll into a log and tuck in the ends securely on both sides; each log should be about 1 ½” x 3”. Place the logs in the baking dish, packing them tightly so that the sides touch; you should have room for about 12 logs.
When the first layer is complete, pour another quarter cup of tomato sauce over it and add the second layer, with the logs placed in the opposite direction, so that each log is not directly on top of another one. Pour the last quarter cup of tomato sauce over the top.
Bake in the preheated oven until the sauce is thick and bubbly, around 20 minutes. Cool slightly but serve hot; include some of the cabbage from the bottom of the baking dish on each plate.